On the product of two $1$-$q$-summable series
Complex Variables
2023-02-24 v1
Abstract
In this paper we consider a -analog of the Borel-Laplace summation process defined by Marotte and the second author, and consider two series solutions of linear -difference equations with slopes and . The latter are -summable and we prove that the product of the series is -(multi)summable and its -sum is the product of the -sum of the two series. This is a first step in showing the conjecture that the -summation process is a morphism of rings. We prove that the -summation does induce a morphism of fields by showing that if the inverse of the -Euler series is -summable, then its -sum is not the inverse of the -sum of the -Euler series.
Keywords
Cite
@article{arxiv.2302.11859,
title = {On the product of two $1$-$q$-summable series},
author = {Thomas Dreyfus and Changgui Zhang},
journal= {arXiv preprint arXiv:2302.11859},
year = {2023}
}